- #1

greypilgrim

- 538

- 36

The capacitance of an ideal plate capacitor (coaxial cable) goes to zero as the plate distance (outer radius) goes to infinity. This doesn't happen with concentric spheres as we let the outer radius go to infinity, hence a single sphere has a nonzero capacitance.

What's the exact reason for this? Does it have something to do with the sphere being truly 3D while a plate is essentially 2D and a cable 1D?

Or is this an artifact of the inconsistency in the derivation of the capacitances of the plate capacitor and coaxial cable? On one hand they assume a finite area/length, on the other they assume the electric field to behave as it would for infinite plates or cables.

Different question: How does one compute the capacitance of an arbitrary conducting 3D shape? Is it always by first assuming an outer shell and then letting it go to infinity? What shape would this shell need to have?

Yet another question: I assume a sphere has the maximum capacitance of some set of conducting 3D shapes, because it has no irregularities where the charge could accumulate and maximize the electric field. What is this set? Is it the set of all 3D shapes with the same volume, or the one of all 3D shapes with the same surface area, or something else?